Newton's Second Law of Motion - Force and Acceleration
5.1 - Force Causes Acceleration
Recalling from Ch. 2, acceleration is described as how quickly motion changes, and can be explained through the equation:
Acceleration = change in velocity/time interval
Without a force being applied to an object, it is impossible for there to be acceleration.
For example:
An object at rest, such as a hockey puck on ice, has no acceleration. However, once a force is applied, such as a push, the puck will have a change in motion, which is defined as acceleration. As the puck is sliding accross the ice, it slides at a constant velocity with no acceleration, but when another stick acts on the puck to catch it, a change in motion will have been made due to the force.
Net Force- the combination of forces acting on an object.
Doubling the force acted on an object will cause twice the amount of acceleration, tripling will cause three times, and so on. Therefore, it can be assumed that:
Acceleration is directly proportional to net force.
5.2 - Mass Resists Acceleration
The relationship between mass and acceleration is inversely proportional, meaning that as the mass of an object increases, the acceleration of that object will decrease, if pushed with a constant force.
Acceleration is directly proportional to 1/mass
5.3 - Newton's Second Law
Newton's Second Law States:
The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object.
-OR-
Acceleration is directly proportional to the net force/mass.
From this relationship, it is shown that doubling the force on the object will double its acceleration, and doubling the mass will halve the acceleration. Doubling both the mass and the force will result in an unchanged velocity.
5.4 - Friction
Friction is a force that acts when two objects come in contact with eachother, and always acts in a direction to oppose motion.
In the presence of friction, an object may move with a constant velocity when there is an outside force acting on it to balance out the friction.
5.5 - Applying Force- Pressure
Pressure is described as the amount of force per unit of area:
Pressure=force/area of application
Pressure is measured in pascals, which are equal to one newton per square meter.
For example:
If you somehow found yourself standing on thin ice on top of a frozen lake, your best chance of not falling through the ice would be to lay down on the ice on your stomach and spread your surace area out as far as possible. This is safer than standing because in a standing position, all of your weight is concentrated through the little surface area of the soles of your shoes. Laying down, your weight is more spread out, lessening the concentration of weight on any given part of the ice.
5.6 - Free Fall Explained
Falling objects will accelerate equally, regardless of their masses.
An example of this concept is shown above, in which you can see the elephant and a feather falling with the same acceleration.
Keeping in mind, a=f/m, it is easy to explain why these two objects accelerate equally:
- Applying Newton's Second law to this situation, we know that the acceleration of an object is directly related to its force and inversely related to its mass.
- Gravity, which is the force of the earth pulling down on the object, is the only force acting on the two objects.
- Therefore, the force on the elephant is much greater than the force on the feather, but remembering Newton's Second Law, we know that mass resists the force.
- Since the mass and weight are equally as much greater than the mass and weight of the feather, they balance out and cause the feather and the elephant to accelerate equally in free fall.
5.7 - Falling and Air Resistance
With the presence of Air Resistance, the situation with the elephant and the feather has somewhat of a different outcome.
Clearly, the elephant still has a much greater weight than the feather in this situation. When we consider the concept of terminal velocity in this situation, however, it can be shown why in the presence of air resistance the feather will fall much slower than the elephant:
- As an object falls and encounters air resistance, the point in time when the air resistance is equal to the object's weight, the object has reached terminal velocity.
- Although both objects are encountering air resistance, the feather will experience terminal velocity much faster because of its such small weight.
- The elephant has a very heavy weight, and will therefore reach terminal velocity much later than the feather, which is why the elephant is able to fall so much faster than the feather in the presence of air resistance.
Ch. 5
Newton's Second Law of Motion - Force and Acceleration
5.1 - Force Causes Acceleration
Recalling from Ch. 2, acceleration is described as how quickly motion changes, and can be explained through the equation:
Acceleration = change in velocity/time interval
Without a force being applied to an object, it is impossible for there to be acceleration.
For example:
An object at rest, such as a hockey puck on ice, has no acceleration. However, once a force is applied, such as a push, the puck will have a change in motion, which is defined as acceleration. As the puck is sliding accross the ice, it slides at a constant velocity with no acceleration, but when another stick acts on the puck to catch it, a change in motion will have been made due to the force.
Net Force- the combination of forces acting on an object.
Doubling the force acted on an object will cause twice the amount of acceleration, tripling will cause three times, and so on. Therefore, it can be assumed that:
Acceleration is directly proportional to net force.
5.2 - Mass Resists Acceleration
The relationship between mass and acceleration is inversely proportional, meaning that as the mass of an object increases, the acceleration of that object will decrease, if pushed with a constant force.
Acceleration is directly proportional to 1/mass
5.3 - Newton's Second Law
Newton's Second Law States:
The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object.
-OR-
Acceleration is directly proportional to the net force/mass.
From this relationship, it is shown that doubling the force on the object will double its acceleration, and doubling the mass will halve the acceleration. Doubling both the mass and the force will result in an unchanged velocity.
5.4 - Friction
Friction is a force that acts when two objects come in contact with eachother, and always acts in a direction to oppose motion.
In the presence of friction, an object may move with a constant velocity when there is an outside force acting on it to balance out the friction.
5.5 - Applying Force- Pressure
Pressure is described as the amount of force per unit of area:
Pressure=force/area of application
Pressure is measured in pascals, which are equal to one newton per square meter.
For example:
If you somehow found yourself standing on thin ice on top of a frozen lake, your best chance of not falling through the ice would be to lay down on the ice on your stomach and spread your surace area out as far as possible. This is safer than standing because in a standing position, all of your weight is concentrated through the little surface area of the soles of your shoes. Laying down, your weight is more spread out, lessening the concentration of weight on any given part of the ice.
5.6 - Free Fall Explained
Falling objects will accelerate equally, regardless of their masses.
An example of this concept is shown above, in which you can see the elephant and a feather falling with the same acceleration.
Keeping in mind, a=f/m, it is easy to explain why these two objects accelerate equally:
- Applying Newton's Second law to this situation, we know that the acceleration of an object is directly related to its force and inversely related to its mass.
- Gravity, which is the force of the earth pulling down on the object, is the only force acting on the two objects.
- Therefore, the force on the elephant is much greater than the force on the feather, but remembering Newton's Second Law, we know that mass resists the force.
- Since the mass and weight are equally as much greater than the mass and weight of the feather, they balance out and cause the feather and the elephant to accelerate equally in free fall.
5.7 - Falling and Air Resistance
With the presence of Air Resistance, the situation with the elephant and the feather has somewhat of a different outcome.
- As an object falls and encounters air resistance, the point in time when the air resistance is equal to the object's weight, the object has reached terminal velocity.
- Although both objects are encountering air resistance, the feather will experience terminal velocity much faster because of its such small weight.
- The elephant has a very heavy weight, and will therefore reach terminal velocity much later than the feather, which is why the elephant is able to fall so much faster than the feather in the presence of air resistance.